Final answer:
To find the monthly payment for Brendan Walsh's $30,000 loan at 6% interest over 60 months, we use an amortization formula. The calculated monthly payment is approximately $580, which suggests there is an error with the provided answer options, as none match this result precisely.
Step-by-step explanation:
To calculate the monthly payment amount for Brendon Walsh's $30,000 loan at a 6% interest rate over 5 years (which is 60 months), we need to use the formula for the monthly payment on an installment loan, which is derived from the amortization formula.
The formula is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = Monthly payment
P = Loan amount ($30,000)
i = Monthly interest rate (Annual interest rate / 12 months)
n = Total number of payments (Loan term in months)
So, i = 6% annually / 12 = 0.005 monthly, and n = 5 years * 12 months/year = 60 months.
Inserting these values into the formula gives us the monthly payment:
M = 30,000 [ 0.005(1 + 0.005)^60 ] / [ (1 + 0.005)^60 - 1 ]
= 30,000 [ 0.005(1.005)^60 ] / [ (1.005)^60 - 1 ]
= 30,000 [ 0.182917 ] / [ 0.349562 ]
= $579.98
Therefore, the correct monthly payment amount is approximately $580, which isn't an option provided in the question, so it seems there may have been an error in the options given. If we look at the closest that fits our result, it would be option c) $650, which could be a rounded figure or an incorrectly calculated option.